TL;DR I used Monte-Carlo simulations + Elo-based win probability estimation to find the probability of Hikaru and other top players scoring very long win streaks (e.g. 55+ consecutive wins) over a year after Kramnik's allegations that Hikaru Nakamura might have cheated based on a number of performances. Initially I thought such streaks are indeed statistical anomalies, but it turned out to be extremely probable: Hikaru scoring at least 55 wins in a row over a course of 3000+ online blitz 3+0 games this year is about 98.4%

That is likely based on large sample size (3k+ games in 3+0 blitz only this year, 35k blitz games over lifetime just on Chess.com), Hikaru being highly skilled (consistently top 1-2 ranked blitz player both over the board and online) and low opposition rating (as compared to other top 5 blitz players on Chess.com: Magnus Carlsen, Nihal Sarin and Daniel Naroditsky).

There's also a discussion and short summary on Reddit (https://www.reddit.com/r/chess/comments/1873ohw/analyzing_hi...)